The formal cell-zeta and formal multiple-zeta algebra conjecture

Let ${\cal FC}$ be the formal cell-zeta algebra and ${\cal FZ}$ the formal multiple-zeta algebra defined using formal iterated-integral symbols modulo the regularised double-shuffle relations. The formal cell-zeta algebra conjecture. The formal algebras ${\cal FC}$ and ${\cal FZ}$ should be isomorphic. This would identify the combinatorial cell-zeta presentation with the classical formal multiple-zeta presentation; no proof or disproof is given in the supplied text.